Coupled mass to matrix problem

Hi, I am new around here. Hope you don't mind me beginning my stay with a question.

1. The Problem

Suppose masses are located at positions in a line and connected by springs with constants whose natural lengths of extension are .

Let denote the rightward forces on the masses, e.g.,

a) Write the 4 X 4 matrix equation relating the column vectors and . Let denote the matrix in this equation.

**2. Attempt at solution**

I treat this as a equilibrium problem. I imagine the masses being pulled to the right and held in place. Then I find the forces neccessary to keep them in that new position. I'm not sure that this is what the problem asks for, but I don't want to just post the question :)

I then expand and simplify each and expression.

I then write these equations in the form:

Sorry about the formatting of matrices, I get too long string errors when I tried writing them next to eachother..

Somehow I feel that the masses should be included in the party as well...

Any suggestions are appreciated, thanks.